If you plan to estimate the Riemannian Metric then when you
compute the Laplacian for best results you should use
laplacian_method = 'geometric' and set the keyword
parameter 'scaling_epps' to the 'radius' that was used
in the affinity method.
First import the class:
'''
from megaman.geometry.rmetric import RiemannMetric
'''
We can then estimate the R metric on each embedding with:
'''
geom.laplacian_method = 'geometric'
geom.laplacian_kwds = {'scaling_epps':radius} # scaling ensures convergence to Laplace-Beltrami operator
laplacian_matrix = geom.compute_laplacian_matrix()
rmetric_spectral = RiemannMetric(embed_spectral, geom.laplacian_matrix)
H_spectral = rmetric_spectral.get_dual_rmetric()
rmetric_ltsa = RiemannMetric(embed_ltsa, geom.laplacian_matrix)
H_ltsa = rmetric_ltsa.get_dual_rmetric()
rmetric_lle = RiemannMetric(embed_lle, geom.laplacian_matrix)
H_lle = rmetric_lle.get_dual_rmetric()
rmetric_isomap = RiemannMetric(embed_isomap, geom.laplacian_matrix)
H_isomap = rmetric_isomap.get_dual_rmetric()
adjacency_method = 'cyflann'
adjacency_kwds = {'radius': radius}
affinity_method = 'gaussian'
affinity_kwds = {'radius': radius}
laplacian_method = 'symmetricnormalized'
laplacian_kwds = {'scaling_epps': radius}
dataname = workingdirectory + '/untracked_data/chemistry_data/tolueneangles020619_pca50'
#dataname = '/Users/samsonkoelle/Downloads/manigrad-100818/mani-samk-gradients/untracked_data/chemistry_data/ethanolangles022119_pca50'
data = np.load(dataname + '.npy')
geom = Geometry(adjacency_method=adjacency_method,
adjacency_kwds=adjacency_kwds,
affinity_method=affinity_method,
affinity_kwds=affinity_kwds,
laplacian_method=laplacian_method,
laplacian_kwds=laplacian_kwds)
geom.set_data_matrix(data)
geom.laplacian_method = 'geometric'
geom.laplacian_kwds = {'scaling_epps': radius}
laplacian_matrix = geom.compute_laplacian_matrix()
geom.compute_laplacian_matrix()
sample = np.arange(0, data.shape[0], 1000)
distorion_vs_rad_dim2 = run_estimate_radius(data,
geom.adjacency_matrix,
sample=sample,
d=1,
rmin=1,
rmax=10,
ntry=50,
run_parallel=True,
search_space='logspace')
np.save(dataname + '_distortionradius', distorion_vs_rad_dim2)
If you plan to estimate the Riemannian Metric then when you
compute the Laplacian for best results you should use
laplacian_method = 'geometric' and set the keyword
parameter 'scaling_epps' to the 'radius' that was used
in the affinity method.
First import the class:
'''
from megaman.geometry.rmetric import RiemannMetric
'''
We can then estimate the R metric on each embedding with:
'''
geom.laplacian_method = 'geometric'
geom.laplacian_kwds = {
'scaling_epps': radius
} # scaling ensures convergence to Laplace-Beltrami operator
laplacian_matrix = geom.compute_laplacian_matrix()
rmetric_spectral = RiemannMetric(embed_spectral, geom.laplacian_matrix)
H_spectral = rmetric_spectral.get_dual_rmetric()
rmetric_ltsa = RiemannMetric(embed_ltsa, geom.laplacian_matrix)
H_ltsa = rmetric_ltsa.get_dual_rmetric()
rmetric_lle = RiemannMetric(embed_lle, geom.laplacian_matrix)
H_lle = rmetric_lle.get_dual_rmetric()
rmetric_isomap = RiemannMetric(embed_isomap, geom.laplacian_matrix)
H_isomap = rmetric_isomap.get_dual_rmetric()
'''